Highest Common Factor of 412, 505, 998 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 412, 505, 998 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 412, 505, 998 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 412, 505, 998 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 412, 505, 998 is 1.
HCF(412, 505, 998) = 1
HCF of 412, 505, 998 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 412, 505, 998 is 1.
Highest Common Factor of 412,505,998 is 1
Step 1: Since 505 > 412, we apply the division lemma to 505 and 412, to get
505 = 412 x 1 + 93
Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 93 and 412, to get
412 = 93 x 4 + 40
Step 3: We consider the new divisor 93 and the new remainder 40, and apply the division lemma to get
93 = 40 x 2 + 13
We consider the new divisor 40 and the new remainder 13,and apply the division lemma to get
40 = 13 x 3 + 1
We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get
13 = 1 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 412 and 505 is 1
Notice that 1 = HCF(13,1) = HCF(40,13) = HCF(93,40) = HCF(412,93) = HCF(505,412) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 998 > 1, we apply the division lemma to 998 and 1, to get
998 = 1 x 998 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 998 is 1
Notice that 1 = HCF(998,1) .
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Frequently Asked Questions on HCF of 412, 505, 998 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 412, 505, 998?
Answer: HCF of 412, 505, 998 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 412, 505, 998 using Euclid's Algorithm?
Answer: For arbitrary numbers 412, 505, 998 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.